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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 88 · 40 questions
TalentJR

How to solve it (Name the topic, then solve): Name the topic first: angles, counting, worst case, probability, digits, mensuration, data, coordinates, AP, algebra, primes or Venn diagrams. Use that lesson’s method; draw a quick sketch, list or Venn diagram on rough paper. Rule out options of the wrong kind — a probability above 1, or a triangle angle of 180° or more. Check by working backwards or with a second method when you can.

NameDateTime takenScore ___ / 40
  1. 1.How many factors does 95 have? (a) 5 (b) 2 (c) 3 (d) 4
  2. 2.A drawer has lots of blue and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 4 (c) 5 (d) 3
  3. 3.What is the sum of the first 5 terms of the AP 5, 9, 13, …? (a) 130 (b) 75 (c) 65 (d) 21
  4. 4.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 8 (d) 13
  5. 5.A canteen sells 4 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 6 (c) 12 (d) 8
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 59° (b) 120° (c) 60° (d) 61°
  7. 7.What is the mode of 18, 6, 1, 1, 1, 18 and 16? (a) 16 (b) 6 (c) 1 (d) 18
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 54? (a) 6 (b) 3 (c) 5 (d) 4
  9. 9.A bag has 6 green, 9 blue and 8 white balls. One ball is taken out without looking. What is the probability that it is green? (a) 17/23 (b) 6/23 (c) 6/17 (d) 1/3
  10. 10.Two angles of a triangle are 40° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 100° (c) 140° (d) 80°
  11. 11.In a class of 44 children, 29 like dance, 18 like music and 10 like both. How many like neither? (a) 10 (b) 8 (c) 17 (d) 7
  12. 12.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
  13. 13.In which quadrant does the point (2, −4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  14. 14.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 8)(x + 9) (c) (x + 1)(x + 72) (d) (x + 1)(x + 16)
  15. 15.What is the distance between the points (1, 7) and (5, 4)? (a) 5 (b) 6 (c) 25 (d) 7
  16. 16.In a class of 39 children, 18 like maths, 31 like science and 11 like both. How many like neither? (a) 12 (b) 2 (c) 11 (d) 1
  17. 17.A bag has 10 green balls and 11 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 2 (c) 21 (d) 12
  18. 18.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
  19. 19.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 7 (d) 10
  20. 20.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 49 (c) 21 (d) 28
  21. 21.In a class of 35 children, 21 like maths, 12 like science and 5 like both. How many like only maths? (a) 7 (b) 16 (c) 23 (d) 21
  22. 22.What is the distance between the points (2, 1) and (17, 9)? (a) 23 (b) 289 (c) 17 (d) 18
  23. 23.What are the roots of x² − 16x + 63 = 0? (a) 1 and 63 (b) 7 and 9 (c) 1 and 15 (d) 3 and 21
  24. 24.The mean of 3 numbers is 39. When the number 51 is added to them, what is the new mean? (a) 45 (b) 42 (c) 39 (d) 43
  25. 25.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 196 (c) 105 (d) 91
  26. 26.Two angles of a triangle are 50° and 120°. What is the third angle? (a) 130° (b) 60° (c) 10° (d) 170°
  27. 27.A bag has 4 black balls and 11 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 6 (c) 15 (d) 5
  28. 28.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 14 (c) 21 (d) 42
  29. 29.A bag has 8 yellow, 9 green and 6 white balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 8/15 (b) 15/23 (c) 1/3 (d) 8/23
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 76? (a) 7 (b) 18 (c) 19 (d) 17
  31. 31.A drawer has lots of white, blue and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 6 (b) 3 (c) 2 (d) 4
  32. 32.What is the mean of 8, 2, 18 and 20? (a) 13 (b) 12 (c) 16 (d) 11
  33. 33.Using (a − b)² = a² − 2ab + b², what is 35²? (a) 1225 (b) 2025 (c) 1575 (d) 1235
  34. 34.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 100° (c) 20° (d) 80°
  35. 35.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 45 (c) 100 (d) 90
  36. 36.What is the mode of 8, 8, 17, 20, 17, 18 and 17? (a) 17 (b) 8 (c) 18 (d) 20
  37. 37.In a class of 37 children, 21 like cricket, 22 like football and 12 like both. How many like neither? (a) 7 (b) 6 (c) 18 (d) 12
  38. 38.In a class of 41 children, 26 like tea, 12 like coffee and 7 like both. How many like at least one of the two? (a) 38 (b) 31 (c) 24 (d) 41
  39. 39.What is the smallest prime factor of 203? (a) 29 (b) 2 (c) 7 (d) 1
  40. 40.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 2/3 (b) 1/4 (c) 1/3 (d) 1/2

Answer key

  1. 4
  2. 3
  3. 65
  4. 7
  5. 8
  6. 60°
  7. 1
  8. 5
  9. 6/23
  10. 100°
  11. 7
  12. 1/2
  13. Fourth quadrant
  14. (x + 8)(x + 9)
  15. 5
  16. 1
  17. 12
  18. 616 sq cm
  19. 7
  20. 21
  21. 16
  22. 17
  23. 7 and 9
  24. 42
  25. 91
  26. 10°
  27. 6
  28. 42
  29. 8/23
  30. 18
  31. 4
  32. 12
  33. 1225
  34. 20°
  35. 45
  36. 17
  37. 6
  38. 31
  39. 7
  40. 1/2

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